Lagrange stability of memristive quaternion-valued neural networks with neutral items

Abstract

This paper concentrates on the global exponential Lagrange stability of memristive quaternion-valued neural networks (MQVNNs) with neutral items. Some classical restrictions on the activation function of neutral item are removed. A new Lyapunov-Krasovskii functional (LKF) including information of neutral items is designed to overcome the difficulty induced by the coexist of quaternions, memristor, and neutral item. Furthermore, in order to reduce the conservativeness, both reciprocally convex inequality and Wirtinger-based inequality are extended to the quaternion domain. Based on the extended inequalities, Lyapunov theory, and novel analytical techniques, concise criteria in the form of linear matrix inequalities (LMIs) are proposed to ascertain the Lagrange stability of the interested MQVNNs. Finally, the correctness and effectiveness of theoretical results are checked by two numerical examples.